Question

How do you solve `3^ { 3r - 1} = 3^ { - 2r - 3}`?

Answer 1

In the given eqn, the bases are equal, so equate powers on both sides.

Explanation:

`3r-1=-2r-3`

`5r=-2`

`r= -2/5`

Answer 2

`r=-2/5`

Explanation:

Since the `color(blue)"bases on both sides of the equation are 3"` we can equate the exponents.

`rArr3r-1=-2r-3`

`rArr5r=-2`

`rArrr=-2/5`

`color(blue)"As a check"`

`3^((-6/5-5/5))=3^(-11/5)`

`"and " 3^((4/5-15/5))=3^(-11/5)`

`rArrr=-2/5" is the solution"`